Are there any benefits or downsides in feeding the children (around elementary school age) on the schedule of "I'm hungry now" as opposed to scheduled meal times?
This is of course assuming that the nutritional content remains the same, e.g. it's not like they demand a piece of cake 1 hr before lunch and then don't eat soup or veggies because of that.
An example would be: they ask for food 1 hour before usual lunch time and get a fruit salad (that they would otherwise get at snack time) because they aren't yet hungry enough for full lunch. Then they eat lunch 1-2 hrs later. Then then demand what would have been dinner during snack (but eat less of it) and then finish the day at usual dinner time with something light like an extra Yogurt. So they get 1 extra meal, with a mild increase in calories, and no decrease in useful nutrition.
My main concern is lack of stable food schedule induced by indulging such demands.
Is that a valid concern as long as I manage the total nutritional input in a sane way?
One of the things that worry me is that during school days they obviously don't have such flexibility for the first 3 meals.
 - The specific kids in question have decent metabolism and are stably UNDER the average weight, so extra calories are NOT an issue. Confirmed with their pediatrician.